IF Mayor Bloomberg wants Assembly Speaker Sheldon Silver to renew mayoral control of the city school system without a confrontation, he had better keep Schools Chancellor Joel Klein as far away from Albany as possible.

Three sources said Silver – who holds life-and-death power over the critical renewal – simply can’t stand the chancellor.

“You can’t mention Klein’s name in Shelly’s presence,” one of the sources said. “He hates him with a passion.”

A second source said there was a sense among some legislators that Klein has “gone out of his way to antagonize them and the speaker.”

Klein and Silver have had their share of run-ins, especially in 2006, when the administration tried to pressure the speaker to release state funds by threatening to renege on a deal to build a school in his lower Manhattan district.

After that showdown, Silver demanded publicly that Bloomberg fire Klein – though it was clear the chancellor had been doing the mayor’s bidding.

A third source said there was no single incident that created the rift between the men. Instead, “there’s a perceived arrogance there [in Klein]. There’s a sense of ‘I don’t need you. You’re a dumb pol.’ Shelly can’t take that.”

An official who knows both men offered another explanation: “You have two guys who both think they’re the smartest guy in the room. Those two guys aren’t going to like each other.”

Klein spokesman David Cantor insisted Klein and Silver have a good working relationship.

“They’ve worked together for many years and have had some disagreements, but the chancellor has great respect for Speaker Silver,” he said.

The state Legislature has until the end of June to decide whether the mayor will continue to run the city’s school system, as he has for the last seven years. Silver has said he supports mayoral control but wants to make changes that would lead to more parental input.